Predictive modelling and understanding how important your last data point is

Hi all.

Using this as a simple example –

There is a fairly basically computer game called Mr Jump.
The aim of the game is to complete the level by finishing the course.
Your game performance is measured in percentage terms, if you complete the level you get to 100%. If you “die” a third of the way through you have completed 33%.
The level will be completed by jumping at the correct time negotiating an obstacle course that is always the same. Obstacles that can get in the way are things like walls to jump over / big jumps / short jumps / series of successive jumps etc etc

Each time you play the game you learn something new, so the more you play the more likely you are to complete the course. However, there are times when you play and due to a mis-click or a loss of concentration you can easily “die” early.

I'm not guaranteeing that a least squares regression line produces the best answer, but the regression equation is % performance = 0.2347998797*attempt number + 5.354915917. To the nearest whole number, it would take 403 attempts to beat the game. Note that a regression equation would predict impossible values over 100 if there were enough attempts. For example, the equation would predict 240% on the 1,000th attempt.